The University of Southampton
University of Southampton Institutional Repository

Geometric dimension of groups for the family of virtually cyclic subgroups

Geometric dimension of groups for the family of virtually cyclic subgroups
Geometric dimension of groups for the family of virtually cyclic subgroups
By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality ℵ n admits a finite‐dimensional classifying space with virtually cyclic stabilizers of dimension n + h + 2 . We also provide a criterion for groups that fit into an extension with torsion‐free quotient to admit a finite‐dimensional classifying space with virtually cyclic stabilizers. Finally, we exhibit examples of integral linear groups of type F whose geometric dimension for the family of virtually cyclic subgroups is finite but arbitrarily larger than the geometric dimension for proper actions. This answers a question posed by W. Lück.
1753-8416
697-726
Degrijse, Dieter
fb33133b-fe90-42a5-8214-409c210906df
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Degrijse, Dieter
fb33133b-fe90-42a5-8214-409c210906df
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6

Degrijse, Dieter and Petrosyan, Nansen (2014) Geometric dimension of groups for the family of virtually cyclic subgroups. Journal of Topology, 7 (3), 697-726. (doi:10.1112/jtopol/jtt045).

Record type: Article

Abstract

By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality ℵ n admits a finite‐dimensional classifying space with virtually cyclic stabilizers of dimension n + h + 2 . We also provide a criterion for groups that fit into an extension with torsion‐free quotient to admit a finite‐dimensional classifying space with virtually cyclic stabilizers. Finally, we exhibit examples of integral linear groups of type F whose geometric dimension for the family of virtually cyclic subgroups is finite but arbitrarily larger than the geometric dimension for proper actions. This answers a question posed by W. Lück.

Full text not available from this repository.

More information

e-pub ahead of print date: 30 December 2013
Published date: 2014
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 360933
URI: https://eprints.soton.ac.uk/id/eprint/360933
ISSN: 1753-8416
PURE UUID: e4a13cd6-1faa-4de1-aefb-b799e62b29d3

Catalogue record

Date deposited: 09 Jan 2014 11:25
Last modified: 16 Jul 2019 21:14

Export record

Altmetrics

Contributors

Author: Dieter Degrijse

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×